Straight Lines and Pair of Straight Lines

If the sum of distances from a point P on two mutually perpendicular straight lines is 1 unit, then the locus of P is a/an

The straight line 3x + y = 9 divides the line segment joining the points (1, 3) and (2, 7) in the ratio

The equations to the pairs of opposite sides of a parallelogram are x2 \(-\) 5x + 6 = 0 and y2 \(-\) 6y + 5 = 0. Find the equations of its diagonals.

The point (\(-\)4, 5) is the vertex of a square and one of its diagonals is 7x \(-\) y + 8 = 0. The equation of the other diagonal is

The number of points on the line x + y = 4 which are unit distance apart from the line 2x + 2y = 5 is

If C is the reflection of A(2, 4) in x-axis and B is the reflection of C in y-axis, then \(|AB|\) is

A line through the point A(2, 0) which makes an angle of 30\(^\circ\) with the positive direction of x-axis is rotated about A in clockwise direction through an angle 15\(^\circ\). Then the equation of the straight line in the new position ...

The coordinates of the foot of the perpendicular from (0, 0) upon the line x + y = 2 are

If C is a point on the line segment joining A(\(-\)3, 4) and B(2, 1) such that AC = 2BC, then the coordinate of C is

If 2a \(-\) 5b \(-\) 3c = 0, show that the straight line ax + by + c = 0 always passes through a fixed point. Find the equation of one straight line passing through this fixed point and parallel to the line 9x + 12y = 20.

The co-ordinates of the foot of perpendicular from (a, 0) on the line \(y = mx + {a \over m}\) are

The distance between the lines \(5x - 12y + 65 = 0\) and \(5x - 12y - 39 = 0\) is

One possible condition for the three points (a, b), (b, a) and (a2, \(-\) b2) to be collinear is